Transition Property for α\alpha-Power Free Languages with α≥2\alpha\geq 2 and k≥3k\geq 3 Letters

In 1985, Restivo and Salemi presented a list of five problems concerning power free languages. Problem $4$ states: Given $\alpha$-power-free words $u$ and $v$, decide whether there is a transition from $u$ to $v$. Problem $5$ states: Given $\alpha$-power-free words $u$ and $v$, find a transition word $w$, if it exists. Let $\Sigma_k$ denote an alphabet with $k$ letters. Let $L_{k,\alpha}$ denote the $\alpha$-power free language over the alphabet $\Sigma_k$, where $\alpha$ is a rational number or a rational "number with $+$". If $\alpha$ is a "number with $+$" then suppose $k\geq 3$ and $\alpha\geq 2$. If $\alpha$ is "only" a number then suppose $k=3$ and $\alpha>2$ or $k>3$ and $\alpha\geq 2$. We show that: If $u\in L_{k,\alpha}$ is a right extendable word in $L_{k,\alpha}$ and $v\in L_{k,\alpha}$ is a left extendable word in $L_{k,\alpha}$ then there is a (transition) word $w$ such that $uwv\in L_{k,\alpha}$. We also show a construction of the word $w$

On the algebraic invariant curves of plane polynomial differential systems

We consider a plane polynomial vector field $P(x,y)dx+Q(x,y)dy$ of degree $m>1$. To each algebraic invariant curve of such a field we associate a compact Riemann surface with the meromorphic differential $\omega=dx/P=dy/Q$. The asymptotic estimate of the degree of an arbitrary algebraic invariant curve is found. In the smooth case this estimate was already found by D. Cerveau and A. Lins Neto [Ann. Inst. Fourier Grenoble 41, 883-903] in a different way.Comment: 10 pages, Latex, to appear in J.Phys.A:Math.Ge

Machine learning algorithms can predict tail biting outbreaks in pigs using feeding behaviour records

Tail biting is a damaging behaviour that impacts the welfare and health of pigs. Early detection of precursor signs of tail biting provides the opportunity to take preventive measures, thus avoiding the occurrence of the tail biting event. This study aimed to build a machine-learning algorithm for real-time detection of upcoming tail biting outbreaks, using feeding behaviour data recorded by an electronic feeder. Prediction capacities of seven machine learning algorithms (Generalized Linear Model with Stepwise Feature Selection, random forest, Support Vector Machines with Radial Basis Function Kernel, Bayesian Generalized Linear Model, Neural network, K-nearest neighbour, and Partial Least Squares Discriminant Analysis) were evaluated from daily feeding data collected from 65 pens originating from two herds of grower-finisher pigs (25-100kg), in which 27 tail biting events occurred. Data were divided into training and testing data in two different ways, either by randomly splitting data into 75% (training set) and 25% (testing set), or by randomly selecting pens to constitute the testing set. In the first data splitting, the model is regularly updated with previous data from the pen, whereas in the second data splitting, the model tries to predict for a pen that it has never seen before. The K-nearest neighbour algorithm was able to predict 78% of the upcoming events with an accuracy of 96%, when predicting events in pens for which it had previous data. Our results indicate that machine learning models can be considered for implementation into automatic feeder systems for real-time prediction of tail biting events

Darboux polynomials for Lotka-Volterra systems in three dimensions

We consider Lotka-Volterra systems in three dimensions depending on three real parameters. By using elementary algebraic methods we classify the Darboux polynomials (also known as second integrals) for such systems for various values of the parameters, and give the explicit form of the corresponding cofactors. More precisely, we show that a Darboux polynomial of degree greater than one is reducible. In fact, it is a product of linear Darboux polynomials and first integrals.Comment: 16 page

Wave Function Microscopy of Quasibound Atomic States

In the 1980s Demkov, Kondratovich, and Ostrovsky and Kondratovich and Ostrovsky proposed an experiment based on the projection of slow electrons emitted by a photoionized atom onto a position-sensitive detector. In the case of resonant excitation, they predicted that the spatial electron distribution on the detector should represent nothing else but a magnified image of the projection of a quasibound electronic state. By exciting lithium atoms in the presence of a static electric field, we present in this Letter the first experimental photoionization wave function microscopy images where signatures of quasibound states are evident. Characteristic resonant features, such as (i) the abrupt change of the number of wave function nodes across a resonance and (ii) the broadening of the outer ring of the image (associated with tunneling ionization), are observed and interpreted via wave packet propagation simulations and recently proposed resonance tunneling mechanisms. The electron spatial distribution measured by our microscope is a direct macroscopic image of the projection of the microscopic squared modulus of the electron wave that is quasibound to the atom and constitutes the first experimental realization of the experiment proposed 30 years ago

Wave-function imaging of quasibound and continuum Stark states

Photoionization of an atom in the presence of a uniform static electric field provides the unique opportunity to expand and visualize the atomic wave function at a macroscopic scale. In a number of seminal publications dating back to the 1980s, Fabrikant, Demkov, Kondratovich, and Ostrovsky showed that this goal could be achieved by projecting slow (meV) photoionized electrons onto a position-sensitive detector and underlined the distinction between continuum and resonant contributions. The uncovering of resonant signatures was achieved fairly recently in experiments on the nonhydrogenic lithium atoms [Cohen et al., Phys. Rev. Lett. 110, 183001 (2013)]. The purpose of the present article is the general description of these findings, with emphasis on the various manifestations of resonant character. From this point of view, lithium has been chosen as an illustrative example between the two limiting cases of hydrogen, where resonance effects are more easily identified, and heavy atoms like xenon, where resonant effects were not observed

Regularity Properties and Pathologies of Position-Space Renormalization-Group Transformations

We reconsider the conceptual foundations of the renormalization-group (RG) formalism, and prove some rigorous theorems on the regularity properties and possible pathologies of the RG map. Regarding regularity, we show that the RG map, defined on a suitable space of interactions (= formal Hamiltonians), is always single-valued and Lipschitz continuous on its domain of definition. This rules out a recently proposed scenario for the RG description of first-order phase transitions. On the pathological side, we make rigorous some arguments of Griffiths, Pearce and Israel, and prove in several cases that the renormalized measure is not a Gibbs measure for any reasonable interaction. This means that the RG map is ill-defined, and that the conventional RG description of first-order phase transitions is not universally valid. For decimation or Kadanoff transformations applied to the Ising model in dimension $d \ge 3$, these pathologies occur in a full neighborhood $\{ \beta > \beta_0 ,\, |h| < \epsilon(\beta) \}$ of the low-temperature part of the first-order phase-transition surface. For block-averaging transformations applied to the Ising model in dimension $d \ge 2$, the pathologies occur at low temperatures for arbitrary magnetic-field strength. Pathologies may also occur in the critical region for Ising models in dimension $d \ge 4$. We discuss in detail the distinction between Gibbsian and non-Gibbsian measures, and give a rather complete catalogue of the known examples. Finally, we discuss the heuristic and numerical evidence on RG pathologies in the light of our rigorous theorems.Comment: 273 pages including 14 figures, Postscript, See also ftp.scri.fsu.edu:hep-lat/papers/9210/9210032.ps.

Comparative Transcriptional Profiling of Bacillus cereus Sensu Lato Strains during Growth in CO2-Bicarbonate and Aerobic Atmospheres

Bacillus species are spore-forming bacteria that are ubiquitous in the environment and display a range of virulent and avirulent phenotypes. This range is particularly evident in the Bacillus cereus sensu lato group; where closely related strains cause anthrax, food-borne illnesses, and pneumonia, but can also be non-pathogenic. Although much of this phenotypic range can be attributed to the presence or absence of a few key virulence factors, there are other virulence-associated loci that are conserved throughout the B. cereus group, and we hypothesized that these genes may be regulated differently in pathogenic and non-pathogenic strains.Here we report transcriptional profiles of three closely related but phenotypically unique members of the Bacillus cereus group--a pneumonia-causing B. cereus strain (G9241), an attenuated strain of B. anthracis (Sterne 34F(2)), and an avirulent B. cereus strain (10987)--during exponential growth in two distinct atmospheric environments: 14% CO(2)/bicarbonate and ambient air. We show that the disease-causing Bacillus strains undergo more distinctive transcriptional changes between the two environments, and that the expression of plasmid-encoded virulence genes was increased exclusively in the CO(2) environment. We observed a core of conserved metabolic genes that were differentially expressed in all three strains in both conditions. Additionally, the expression profiles of putative virulence genes in G9241 suggest that this strain, unlike Bacillus anthracis, may regulate gene expression with both PlcR and AtxA transcriptional regulators, each acting in a different environment.We have shown that homologous and even identical genes within the genomes of three closely related members of the B. cereus sensu lato group are in some instances regulated very differently, and that these differences can have important implications for virulence. This study provides insights into the evolution of the B. cereus group, and highlights the importance of looking beyond differences in gene content in comparative genomics studies